Direct Proof of the Covariance of Gupta's Indefinite Metric in Quantum Electrodynamics

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Abstract
Gupta's method of the indefinite metric is at this time for many purposes the most satisfactory method of formulating the principles of quantum electrodynamics. Gupta's indefinite metric, however, depends on the number of scalar photons. This number is no invariant. Yet, the covariance of Gupta's indefinite metric has been proved before. This seems at first surprising. In the present paper we show why the lack of invariance of the number of scalar photons does not matter and how a certain covariance of the occupation numbers together with "repolarization operators" insures the covariance of Gupta's method. In particular, if the norms of the eigenfunctions of occupation numbers are chosen in accordance with Gupta's prescription in one Lorentz frame, they are automatically in accordance with this prescription in a different Lorentz frame.